vv<* would like to investigate thr influence of semiconductor material US<*<1 for construct ion of a DFB laser with two sections oil the characteristics of generated impulse'

VNU, JOURNAL OF SCIENCE. Mathematics - Physics. T XVIII, N()2 - 2002

T H E I N F L U E N C E O F M A T E R I A L P A R A M E T E R S IN D F B L A S E R O N G E N E R A T E D I M P U L S E

D in h V a n H o a n g

D t'jm rtim 'ni <>l riiy s ic s . C o llccg v o f S cicn ce - V N V Pham Van Hanh

Hrimti P o ly te ch n ic In s t itu te 1 Introduction

Distributed Fmlback lasn (DFB laser) is (>IH‘ of useful light sources generating

laser radiation vised widoly in optical communication. 1 his laser can generate longitudi­

nal single 1 1 1 0(1«* and it* wavelength is easily modulated. Especially, the DFB ^laser with two (or more) sortions reveals a groat, convenience to optical communication and to all

o p ti c a l transformation. Therefore, to now this laser concentrates the attention ol many

lo s r n r c h in g g r o u p s o n th e w o r ld a n d m a n y w o rk s r e l a t e d w i t h t h i s field a r e p u b li s h e d [1-8

In this paper. vv<* would like to investigate thr influence of semiconductor material US<*<1

for

construct ion of a DFB

laser

with two sections oil the characteristics of generated impulse'. Starling on I ho rate equation approximation, we have established a •systf'in oi (’quations describing the changes of the carrier densities in tho two sections and of I hí' laser photon density versus time, as present <‘(1 in section 2. For determining I ho influona1 of semicondtK tor ^{m aterial} \vr notice th(' ^change of refraction index ot material, and of confincinoiit factors (P ete rm a n coefficients) in each section. The received results arc presented ill section 3. Finally, the* discussion and conclusions are given in section 4.

2. T h e b a s ic e q u a t io n s

A modeling schema, for a DFB laser with two sections is presented in Fig. 1.

Fi gi

Hero, cell A containing actiVO medium designs active cell, but cell B having injection current /o smaller than ¹¹ in roll A takes a role as a saturable absorber ceil. System of equations describing the transient operation of laser is, as in [7]:

I, h

ÌầtCĩ

19

= A - - 7/1— g(u)o - 0 J j ) r i j ~ 71 Wi, (1)

(It eVi n eff

d Nr = " 7 7 - r n — g{^0 - V j ) r i j - 7 2 N 2, (2 )

(11 eV2 n eff

—7 7- = (I'l'/I + r 2//2) — <7 ( ^ 0 - Wj)(n, + 1) - 7 n3 + ị i ự n j P ( u ) . (3)

(it ĩ l eỊf

Here N \, No - carrier density in cells A , B \ r ij - photon density; Co, e - velocity of light in vacuum and electric charge of electron; V i , V2 - volume of cells -4, D \ neff - refraction index of material is seen to 1)<> the same for two cells; ĨỊ, - amplification coefficient of each cell, depending which on carrier density in form:

TỊ i = C k j N i 4* L Ỉ Ị, ( 4 )

here (1, ' t ị - material coefficients; 7 1 , 7 2 - relaxation coefficients of carrier density also (lt*prii(.liug (>I) carrier density as following function:

B o N i _ { B o N2

0 1 ^{1 . n »» J} w)

1 + ^{1 3}1 iV 1 1 -f* jV2

with - niHtmnl coefficients; £ - saturation (oHfiruuit designing tli(* different relaxation of crHTHT (Irnsity between two cells; F ijl’V confinement factors or Peterman coefficients of .4, B colls, rc'sprctivoly. The relaxation coefficient of photÍ>11 7 is d(‘tm niii(i(l by expression:

7 = — (ttttac + b a ex 4- Cờmirr). (6 ) tteff

Here a ,/)/’ - material corffidonts; a ac,QeXia mirr- photon loss at active, absorber coll, and through mirrors, respectively. Function c j ( u o - i j j j ) - characterizing the spectral broadening of laser radiation has form:

» ("" = p + 4 ( ^ - u . , ) 2 = 7 m * ’ 1 7 1

1 + I r j

with r- tho lino width; A , = 2 /u > i)~ u )j/ - detuning coefficient.; angular frequowy at center of line contour and at 7th mode. Moreover, unity in ( j i j + 1) designs t.ho presence of spontaneous omission in laser operation. The last factor in equation (3) notices the inter­

action between external optical signal having power ^{P { u )} with laser radiation, interaction coefficient ị i will bo given unity in examination afterwards. System of equations (1) - ÚÍ) is solved numerically following Runge- Kutta method and the values of all parameters ,\rv

taken following the experimental ones of Junichi Kinoshita on the basis of semiconductor material InGaAsP |9j.

T h e i n f l u e n c e o f m a t e r i a l p a r a m e t e r s i n 21

3 . T h e in f lu e n c e o f some m a t e r ia l p a r a m e t e r s

In our examination, we study only the resonance case in which the generating mode frequency u/j coincides with UJQ. Therefore function g {u>0 — u/j) = 1 . Other values of parameters will he taken as follows: C o = 3.101 0 cm/s, e = l,6 10 “ 19c , V\ z= v2 =

8.4.l ( r9 fill3. Bo = 1 0 10. B ] B> = 1 0 ~8S, £ = 0 .1, 0, = 0 = 4.1()-|r,, r1 0.5, r-2 0 . 2 , /ị ' 10 2A , I o 2.10 5u4,P(a/) = 10U) (p h o to n s/c m 3.s), a = 0.3, ft =

0.7, r = 17,o„, 10()r7i? " 1, (YCJ. 2()()r/7i'"1,a mirr = 1 A c m ~ l } n ef f — 3.4 for two sections

A and IỈ. The received function II ,( t ) ,from solving method indicated above, is presented in fig.2a. Bv using the Fast Fourrier Transformation (FFT ) method we also have function

7 ỉ j ( u s ) given in Fi^.2b.

Kr&fl : ; rj

ipR I ifciiiiiiMiii ỈM^IÉIỈÌÉ^M ■ 1 M B I I I I ‘I HI... Fig.2a

« ' 1 ; v> ^

(■ t i v

lijÇ’iI'ü' ^J 'j

Ct**vV li * ^

s ï ï i ” ' ' 1 1 1

• I.'-' :

A'1’ .*;1 :'•&*

i l i ỉ B Ị

^{I »; ■ ■ ■}

Fig,2 b

All transformations of functions 7ij(t) _or nj(cj) will display clearly the change of pulse characteristics under the influence of diverse dynamical parameters .

1. The influence of refraction index neff

In order to examine the influence» of refraction index in two cells, we choose t hree values of n vt f ( - 3: 3.4; 4) and r o m a i n constant all other values. By the same numerical method w<* have received different graphics of functions U j( t ) and r ij( u ỉ) which presented in Fig. 3 and Fig.4.

T h e i n f l u e n c e o f m a t e r i a l p a r a m e t e r s i n 23

From these fi^uirs wc scr thfit tho pulse characteristics like* the time interval of pulse generation A t . ! hi* it ÌOĨ1 Yiìtt' of pulse frequency A / and the maximum valur of

the first Ị >uls« * intensify I) lire transform ed as seen ill Ta hip 1.

T a b le 1

n„i A I A f I,(in a.u.)

3.0 0.11x10*5 3.3G H z 1.8 x1 0 “’

3.4 0.12x1 ( V s 3 G H z 1.9x1 O'"

4.0 0 .1 6x1 0ks 2.2H z 4.7 x 1 0 '"

...

2. The influrncr of IYterman coefficient Ti in cell A.

In this case wo have taken three values of r x (= 0.3:0.5;0.G). Repeating the analo­

gous method of calculation, till' obtained results about the change of pulse characters are presented 111 Table 2.

T a b le 2

r, A t A f I,(in a.u.)

0.3 0.15x1 ^{(Vs 2 .0 G H z} 0.85.x I O'"

0.5 0 .^12x 10HS ^{3.0 G H z} 1.90x10'°

0 . 6 0. lOx 10 Ns 3.5 G H z 2 .1 0 x 1 0 ’"

3. The influence of Peterman coefficient T2 in cell D.

We have given r*2 throe values as r2 = 0.1;0.2;0.3. The results, that are deduced from graphics of functions ĩ ĩ j ( t ) and Tij(üj). also display the transformation of pulse char­

acters as presented in Tttblo 3.

T a b le 3

r . A t A f I, (in a.u.)

0.1 0 .1 0 x 1 0 "s 3 .0 G H z 2 .6 x 1 0 ’°

0.2 0 .1 1 X10 Ss 3 .0 G H z 1.9x1 o'"

0.3 0 .1 2 x 1 0 -*s 3 .0 G H z 1.4x10-°

4. Discussion and conclusions

From the changes of graphics of functions ⁷i j ( t ) yT ij( u ) like from the values in the Tables we can reveal some interesting remarks:

1. The augmentation of refraction index of semiconductor material in two sections results in the incroasr of pulse intensity I \ like of time interval of pulse generation A £,

hut frequency r e p e t i t i o n rate A / is decreased. This means that for caçh semiconductor material of constructing DFB laser, one need choose the suitable value of refraction index in order to benefit both the frequency repetition rate as well as the pulse intensity.

2. Peterman coefficients in two sections have contrary influence on pulse characters.

The increase of this coefficient in section A (i.e. the increase of r ị) leads to the decrease of time interval of pulse generation and the increase of pulse intensity, while the augmentation of r2 in section Ỉ Ì leads to the increase and decrease of corresponding quantities cited above. In other words, the role of these Peterman coefficients is opposite. Therefore*, choosing apprgpriate injection currents for two sections will be an important problem in the use of DFB laser with two sections in optical communication. This character of Peterman coefficients is also seen in the stationary operation of DFB laser [7].

3. It is necessary to notice that, all graphics of functions n j ( t ) } rij(u j) received hero • is deduced from parameter values given above. Clearly, they don’t display stable pulses for a long time (some ten ns). This also means that used parameter values are not preferable.

However, tilo change of pulse characters indicated here still reveals the influence of material parameter in the use of DFB laser with two sections in all optical transformation.

References

1. h : Wenzel et al., I E E E J . Q E , Vol. 32, 1(1996). p 69.

2 . B. Sartorius et al., I E E E J. Q E. Vol. 33, 2(1997), p 2 1 1 . 3. G. Mort hier.. I E E E J. Q E , Vol. 33, 2(1997), p 231.

4. J.D. Freeze et al., I E E E J . Q E, Vol 33, 8(1977), p 1253.

5. K. Otsuka et al., Phys. Rev. A Vol. 60, 5(1999), p 3389.

6 . Siao-Lung Hwong et al., O p tics Letters,Vol. 25, 9(2000), p 646.

7. Dinh Van Hoang et al., M o d e m Problem s in O ptics a n d Spectroscopy. Torn. II, (2 0 0 0.) p 406.

9. Junichi Kinoshita., I E E E J . Q E , Vol. 30\ (1994), p 929.

TẠP CHÍ KHOA HỌC ĐHQGHN, Toán - Lý. T.xvm, Số 2 - 2002

Ả N H H U Ở N G C Ủ A C Á C T H A M s ố V Ậ T LIỆU T R O N G L A ZE DFB LÊN X U N G P H Ấ T

Đinh Vùn Hoàng

Khoa Vật lý, Dại học Khoa học T ự nhiên - ĐHQG Hà Nội

Phạm Vân Hạnh

Trường Đại học Bách Khoa Hà Nội

Trong bài báo này đã được tim thấy ảnh hường của một số tham số vật liệu như hệ số Peterman» chiết xuất chất bán dản... lên các đặc trưng của xung phát, khi dựa vào lời giải bằng số theo phương pháp Runge - Kutta, của hệ phương trình mỏ tả sự hoạt động

khống dừng của một DFB laser ^{2 ngăn .}